Fractional-order dynamic modeling and parameter optimization of powertrain magnetorheological suspension systems

To address increased powertrain vibration transmission and limited adaptability of passive mounts in lightweight armored vehicles, this study proposes a road-condition-oriented parameter design method for a magnetorheological (MR) hybrid suspension system based on generalized fractional order dynamic modeling. A fractional-order Kelvin–Voigt model is first established for the MR mount by introducing fractional stiffness and damping terms to describe its memory-dependent and broadband nonlinear behavior. Shaking-table tests are used to verify that the proposed model more accurately characterizes the frequency-dependent dynamic response of the MR mount than the conventional integer-order Kelvin–Voigt model. A half-car four-degree-of-freedom dynamic model is then developed by considering the vertical and pitch motions of both the powertrain and vehicle body. V12 engine excitation and Class B, D, and E random road excitations are incorporated to analyze the vibration transmission characteristics of the powertrain MR suspension system. Based on this model, Simulink Design Optimization is used to optimize the mount parameters, with the normalized weighted root mean square of acceleration as the objective function. The optimized parameter sets for Class B, D, and E roads achieve minimum objective-function values of 0.1137, 0.1245, and 0.1243 under their corresponding road conditions, respectively. Cross-condition comparisons show that parameters optimized for one road class do not always provide the best performance under other road excitations; in the Class E case, the objective-function value decreases from 0.2206 with Class B optimized parameters to 0.1243 with Class E optimized parameters. The results demonstrate that optimal MR mount stiffness and damping parameters are strongly road condition dependent, providing a theoretical reference for parameter matching of powertrain MR suspension systems.